Name ———————————————————————
Date ————————————
Practice A
LESSON
3.3
For use with pages 148 –153
Check whether the given number is a solution of the equation.
1. 6x 1 1 2 5x 5 7; 2
1
3. } (8x 2 6) 5 1; 1
2
2. 7 1 2(m 2 4) 5 3; 1
State the first step in solving the equation.
4. 13y 1 7y 2 6 5 11
5. 5(a 2 4) 5 44
1
6. } (m 2 4) 5 5
3
7. 7 1 6(w 2 3) 5 31
8. 8d 2 4 2 6d 5 22
9. 7 2 3( p 1 6) 5 27
Solve the equation.
10. 3a 1 2a 1 7 5 12
11. 9n 2 4 1 n 5 16
12. 7c 1 3 2 5c 5 15
13. 16 2 3y 1 4y 5 27
14. 2 1 3(x 1 1) 5 17
15. 15 1 4(m 2 2) 5 21
16. 2p 1 3( p 1 3) 5 21
17. 6w 1 5(w 2 2) 5 23
18. 7 2 3(x 1 2) 5 4
1
19. } (d 2 5) 5 1
4
1
20. } (m 1 6) 5 4
3
1
21. } (w 2 7) 5 5
8
Find the value of x for the triangle or rectangle.
22. Perimeter 5 17 feet
5 ft
xm
2x ft
2x m
24. Target Heart Rate The target heart rate is the heartbeat rate during aerobic exercise
that provides a benefit to your heart. The target heart rate for a person exercising at
70% intensity is given by the equation y 5 0.7(200 2 x) where y is the target heart
rate in beats per minute and x is the person’s age in years.
a. How old is a person with a target heart rate of 133 beats per minute?
b. How old is a person with a target heart rate of 126 beats per minute?
25. Spare Change You have quarters and nickels saved in a piggy bank. There is a total
of $3.45 in quarters and nickels and there are 9 more nickels than quarters.
a. Use the verbal model to write an equation that you can use to find the number of
nickels and quarters in your piggy bank. Let q represent the number of quarters.
Number of
quarters
p
Value of
1 quarter
1
Number of
nickels
p
Value of
1 nickel
5
Total amount
in piggy bank
LESSON 3.3
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
x ft
23. Perimeter 5 18 meters
b. How many nickels and quarters are in the piggy bank?
Algebra 1
Chapter 3 Resource Book
29
Name ———————————————————————
LESSON
3.3
Date ————————————
Practice B
For use with pages 148 –153
Solve the equation.
1. 16x 2 15 2 9x 5 13
2. 15m 1 4 2 9m 5 232
3. 3b 2 9 2 8b 5 11
4. 231 5 8 2 6p 2 7p
5. 9 1 4(x 1 1) 5 25
6. 7(d 2 5) 1 12 5 5
7. 10a 1 5(a 2 3) 5 15
8. 19a 2 3(a 2 6) 5 66
1
9. } (x 2 8) 5 7
4
1
10. } (d 1 9) 5 212
3
3
11. } (n 1 3) 5 9
4
5
12. 2}(w 2 1) 5 15
2
13. 6.4 1 2.1(z 2 2) 5 8.5
14. 4.5 2 1.5(6m 1 2) 5 6
15. 15 5 4.3n 2 2.1(n 2 4)
Find the value of x for the triangle or rectangle.
16. Perimeter 5 23 feet
17. Perimeter 5 24 meters
(x + 3) ft
x ft
(x + 3) m
2x ft
2x m
18. Wrapping a Package It takes 70 inches of ribbon to make a bow and wrap the
x
14 in.
19. Vacation You are driving to a vacation spot that is 1500 miles away. Including rest
stops, it takes you 42 hours to get to the vacation spot. You estimate that you drove at
an average speed of 50 miles per hour. How many hours were you not driving?
20. Moving You helped a friend move a short distance recently. The friend rented a
LESSON 3.3
truck for $15 an hour and rented a dolly for $5. Your friend paid a total of $80 for the
rental. For how long did your friend rent the truck?
21. Painting You and your friend are painting the walls in your apartment. You estimate
that there is 1000 square feet of space to be painted. You paint at a rate of 4 square
feet per minute and your friend paints at a rate of 3 square feet per minute. Your
friend shows up to help you paint 45 minutes after you have already started painting.
a. Write an equation that gives the total number of square feet y as a function of the
number of minutes x it takes to paint all of the walls.
b. How long will it take you and your friend to finish painting? Round your answer
to the nearest minute.
30
Algebra 1
Chapter 3 Resource Book
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
ribbon around a box. The bow takes 32 inches of ribbon. The width of the box is
14 inches. What is the height of the box?
Name ———————————————————————
LESSON
3.3
Date ————————————
Practice C
For use with pages 148 –153
Solve the equation.
1. 23x 2 8 2 14x 5 10
2. 46m 1 11 2 33m 5 228
3. 5b 2 17 2 13b 5 7
4. 29 5 27 2 11p 2 13p
5. 23 1 5(x 1 4) 5 47
6. 6(2d 2 1) 1 13 5 19
7. 34a 2 4(5a 1 2) 5 36
8. 5a 2 4(3a 1 7) 5 221
3
9. } (x 2 5) 5 12
4
3
10. } (5m 1 15) 5 212
5
5
11. } (2p 2 1) 5 32
8
7
12. 2} (3w 2 2) 5 221
3
13. 5.8 1 3.5(z 2 4) 5 9.3
14. 5.4 2 3.1(4m 1 3) 5 45.7
15. 16 5 6.5n 2 3.3(2n 2 5)
Find the value of x for the triangle or rectangle.
16. Perimeter 5 32 feet
x ft
17. Perimeter 5 24 meters
(x + 7) ft
(x + 1) m
(3x + 1) m
3x ft
18. Class Reunion You are traveling 180 miles back to your home town for a class
19. Retaining Wall You and two friends are building a retaining wall. The estimate for the
number of blocks in the wall is 500 blocks. You and one of your friends have experience
building retaining walls, so you each can install 20 blocks per hour. Your other friend,
who is doing this for the first time, can install about 8 blocks per hour. You had a dentist
appointment and showed up 1 hour after your friends started on the wall. How long will
it take you to build the wall? Round your answer to the nearest hour. How many blocks
will each of you install?
20. Installing Shelves You are hanging 3 display shelves with the same width on a wall
so that there is 18 inches of space above each shelf for placing items. Each shelf
is 3 inches wide. You want the space from the ceiling to the top 18 inches of space
and the space below the bottom shelf to a chair rail to be the same. Determine the
distance from the ceiling to the bottom of each of the shelves so that you can install
them. Explain how you got your answer.
LESSON 3.3
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
reunion. About 60 miles of the trip are through areas where the speed limit is
45 miles per hour and the rest of the trip is through areas where the speed limit is
55 miles per hour. Assuming that you can travel at the speed limits to get to the
reunion, how long will it take you? Round your answer to the nearest tenth.
18 in.
18 in.
71 in.
18 in.
Algebra 1
Chapter 3 Resource Book
31
Name ———————————————————————
LESSON
3.3
Date ————————————
Challenge Practice
For use with pages 148 –153
In Exercises 1– 6, use n to represent an integer, 2n to represent an even
integer, and 2n 1 1 to represent an odd integer.
1. Find three consecutive integers whose sum is 48.
2. Find three consecutive even integers whose sum is 66.
3. Find three consecutive odd integers whose sum is 99.
4. Find four consecutive integers whose sum is 94.
5. Find four consecutive even integers whose sum is 148.
6. Find four consecutive odd integers whose sum is 72.
7. Manuel has pennies and nickels with a total value of $1.15. The number of nickels
is 43 less than the number of pennies. How many pennies does Manuel have?
8. Alicia has five times as many dimes as she has quarters. Combined the dimes and
quarters total to $9.75. How many dimes does Alicia have?
9. Lola has twice as many quarters and half as many nickels as does Ellen. Ellen has
LESSON 3.3
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
$6.30 in quarters and nickels and has 6 less nickels than quarters. How much money
does Lola have?
36
Algebra 1
Chapter 3 Resource Book
Name ———————————————————————
LESSON
3.3
Date ————————————
Problem Solving Workshop:
Using Alternative Methods
For use with pages 148–153
Another Way to Solve Example 5 on page 150
Multiple Representations In Example 5 of page 150, you saw how to solve
a problem about bird migration using a verbal model. You can also solve the problem by
solving a simpler problem.
PROBLEM
Bird Migration A flock of cranes migrates from Canada to Texas. The cranes take
14 days (336 hours) to travel 2500 miles. The cranes fly at an average speed of
25 miles per hour. How many hours of the migration are the cranes not flying?
METHOD
Solving a Simpler Problem You can solve the problem by solving a simpler problem.
STEP 1
Write an equation for the amount of time the cranes are flying. Let h be the
amount of time the cranes are flying.
Distance
(miles)
2500
Rate
Time spent flying
5 (miles/hour) p
(hours)
5
25
p
h
An equation for the amount of time the cranes are flying is 2500 5 25h.
Find the amount of time the cranes are flying.
2500 5 25h
100 5 h
Write equation.
Divide each side by 25.
The cranes were flying for 100 hours of the migration.
STEP 3
Find the amount of time the cranes were not flying by subtracting the length of
time of the migration by the amount of time flying.
336 2 100 5 236
The cranes were not flying for 236 hours of the migration.
PRACTICE
1. Swimming Amanda swims at an
3. Jogging Mark works out for
average rate of 72 meters per minute.
It takes her 36 minutes to finish
1800 meters with breaks. How many
minutes did Amanda swim? How
many minutes of breaks did she take?
Solve this problem using two
different methods.
50 minutes by biking and jogging.
He bikes at an average rate of
1200 feet per minute and jogs at an
average rate of 900 feet per minute.
He wants to travel a combined 10 miles
(1 mile 5 5280 feet). How many
minutes did Mark spend jogging?
2. What If? Suppose in Example 1 that
4. Perimeter The sides of a triangle have
Amanda wants to swim 2700 meters
and finish in 45 minutes. How many
minutes of breaks did she take?
lengths (3x 1 1) feet, (2x 2 3) feet, and
x feet. The perimeter of the triangle is
22 feet. Find the value of x.
Algebra 1
Chapter 3 Resource Book
LESSON 3.3
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
STEP 2
35
Name ———————————————————————
LESSON
3.3
Date ————————————
Graphing Calculator Activity:
Solving a Linear Equation
For use before Lesson 3.3
QUESTION
How can you use a graphing calculator to solve a linear
equation graphically?
You can solve a linear equation by graphing each side of the equation. The x-value
where the graphs intersect is the solution of the equation.
EXAMPLE
Solve a linear equation graphically
Use a graphing calculator to solve 12 1 x 5 7 graphically.
STEP 1
Enter each side of the equation.
Press Y= . Enter the left side of the equation as y1
and the right side of the equation as y2.
Set window.
The screen is a “window” that lets you look at part
of a graph. Press WINDOW . A friendly window for
y1 and y2 is 210 ≤ x ≤ 10 and 210 ≤ y ≤ 10.
Note that you can also obtain this window by
pressing ZOOM 6.
STEP 3
Graph and solve.
Press 2nd [CALC] 5 to graph y1 and y2 and to find
the point of intersection. The x-value of the point of
intersection is the solution of the linear equation.
From the graph, you can see that the x-value is 25.
Check this answer in the original equation.
PRACTICE
WINDOW
Xmin=-10
Xmax=10
Xscl=1
Ymin=-10
Ymax=10
Yscl=1
Xres=1_
Intersection
X=-5
Y=7
Solve the equation graphically. Use the window given in the example.
1. x 2 4 5 5
2.
2x 1 7 5 23
3. 7 5 5x 2 1 2 x
4. 28 5 7x 1 22 2 2x
5.
5(2x 2 7) 2 3x 5 7
6. 5 5 0.5(x 1 13)
7. 24x 1 3(x 2 1) 5 6
8.
24.5 5 x 1 2(4 2 3x) 9. 1.2(3 2 x) 1 7 5 4.6
Algebra 1
Chapter 3 Resource Book
LESSON 3.3
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
STEP 2
Plot1 Plot2 Plot3
\Y1=12+X
\Y2=7
\Y3=
\Y4=
\Y5=
\Y6=
\Y7=
27
Name ———————————————————————
Date ————————————
Graphing Calculator Activity:
Solving a Linear Equation continued
LESSON
3.3
For use before Lesson 3.3
TI-83 Plus
Y=
12
ENTER
Casio CFX-9850GC Plus
X,T,,n
ZOOM
6
2nd
ENTER
7
[CALC] 5
From the main menu, choose GRAPH.
12
LESSON 3.3
28
X,,T
EXIT
F6
7
EXE
SHIFT
F5
EXE
SHIFT
F3
F5
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
F3
Algebra 1
Chapter 3 Resource Book
Name ———————————————————————
LESSON
3.3
Date ————————————
Study Guide
For use with pages 1482153
GOAL
EXAMPLE 1
Solve multi-step equations.
Solve an equation by combining like terms
Solve 17x 2 11x 1 8 5 20.
Solution
17x 2 11x 1 8 5 20
Write original equation.
6x 1 8 5 20
Combine like terms.
6x 1 8 2 8 5 20 2 8
Subtract 8 from each side.
6x 5 12
Simplify.
6x
6
Divide each side by 6.
12
6
}5}
x52
Simplify.
Exercises for Example 1
Solve the equation. Check your solution.
1. 9x 2 13x 1 7 5 31
3. 15x 2 9 2 8x 5 12
4. 18 2 2x 2 4x 5 224
EXAMPLE 2
Solve an equation using the distributive property
Solve 4x 1 3(2x 2 1) 5 17.
Solution
METHOD 1 Show All Steps
4x 1 3(2x 2 1) 5 17
4x 1 6x 2 3 5 17
10x 2 3 5 17
LESSON 3.3
10x 2 3 1 3 5 17 1 3
32
10x 5 20
10x
10
20
10
}5}
x52
Algebra 1
Chapter 3 Resource Book
METHOD 2 Do Some Steps Mentally
4x 1 3(2x 2 1) 5 17
4x 1 6x 2 3 5 17
10x 2 3 5 17
10x 5 20
x52
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
2. 13 2 5x 1 8x 5 22
Name ———————————————————————
LESSON
3.3
Study Guide
Date ————————————
continued
For use with pages 1482153
Exercises for Example 2
Solve the equation. Check your solution.
5. 3(x 2 4) 1 4x 5 16
6. 9x 2 6(3x 2 3) 5 9
7. 22x 1 7(3x 21) 5 31
8. 5(2x 1 8) 2 6x 5 16
EXAMPLE 3
Multiply by a reciprocal to solve an equation
3
Solve }
(5x 2 4) 5 12.
4
Solution
3
} (5x 2 4) 5 12
4
4
3
3
4
4
3
} p } (5x 2 4) 5 } p 12
5x 2 4 5 16
x54
4
3
Multiply each side by }3, the reciprocal of }4 .
Simplify.
Subtract 4 from each side.
Simplify.
Exercises for Example 3
Solve the equation. Check your solution.
1
9. } (x 2 11) 5 9
2
3
10. 2} (2y 1 6) 5 15
2
5
11. 215 5 } (4z 2 1)
7
3
12. 36 5 2} (5m 1 12)
4
LESSON 3.3
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
5x 5 20
Write original equation.
Algebra 1
Chapter 3 Resource Book
33